A simple extension of the SM can be possible by an additional \(U(1)\)  gauge symmetry [1]}
which predicts a neutral BSM gauge boson (\(Z^\prime \) ).
This extra gauge boson has been searched for at the Tevatron [2]}, [3]}, LEP [4]}, [5]}, [6]} and LHC [7]}, [8]} with final state dileptons/dijes.
With the precision experiments by the LEP experiment, the strong constraints on the \(Z-Z^\prime \)  mixing
has been studied in [9]}, [10]}.
The collider phenomenology of the \(Z^\prime \)  boson has been intensively studied (see, for example,
[11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]})
with the final state leptons and quarks.
Apart from the pair fermion productions, another important process to study the \(Z^\prime \)  boson
is an associated production of the SM Higgs boson (\(h\) ) with the SM \(Z\)  boson,
such as \(pp\rightarrow Z^\prime \rightarrow Z h\)  at the LHC,
which can arise from a trilinear coupling \(Z^\prime -Z-h\)  if the SM Higgs doublet has an extra \(U(1)\)  gauge charge.
